Problem Description

Given a positive integer $n$, factorize $n$ into prime factors.

Let $n = p_1 \times p_2 \times p_3 \times \dots \times p_x$, where each $p_i$ is a prime number.

If all $p_i$ are odd, then $n$ is called a “Zhi Factor Number” (“只因数”).

Now, given several values of $n$, determine whether $n$ is a “Zhi Factor Number”.

Input Format

This problem contains multiple groups of testdata within a single test case.

The first line contains an integer $T$, the number of testdata groups.

The next $T$ lines each contain an integer $n$, representing one group of data.

Output Format

For each group of data, output one string per line. If $n$ is a “Zhi Factor Number”, output Yes; otherwise output No.

5
2
3
4
6
9

No
Yes
No
No
Yes

Hint

Constraints

There are $10$ test points in total. For the $i$-th test point, $T = \max(1, i - 1)$.

• For $30\%$ of the data, $n \leq 3$.
• For $50\%$ of the data, $n \leq 10$.
• For another $10\%$ of the data, $n$ is odd.
• For another $10\%$ of the data, $n$ is even.
• For $90\%$ of the data, $n \leq 10^9$.
• For $100\%$ of the data, $1 \leq T \leq 9$, $2 \leq n \leq 10^{18}$.

Notes

There are two additional sample files for this problem. See ibvl.zip in the attachments.

Translated by ChatGPT 5